Spin Of The Proton And Axial Charges Of Other Octet Baryons In Chiral Effective Field Theory

After EMC measured that the quark spins contribute only a small fraction of the proton’s spin, almost zero, in polarized deep inelastic scatting experiment in 1988, CERN, DESY, JLab, RHIC and SLAC continued to measure the structure of the proton. Today the experimental measurements indicate that the nucleon’s flavor singlet axial charge 0a（it is interpreted as the proton spin content） measured in polarized deep inelastic scattering is about 0.35 at 23 Ge V. Unlike the early EMC result, this value is still too small compared with early quark models. In the static quark model, quark spin contributes 100% of the proton’s spin. Relativistic quark models predict about 60% of the proton’s spin should be carried by the quarks, with the remaining 40% in quark orbital angular momentum. Where is the “lost” spin of quarks? This is called the proton spin crisis or the spin puzzle. It inspired a vigorous global program of experimental and theoretical developments to understand the internal spin structure of the proton extending for nearly three decades.To understand the proton’s longitudinal spin structure, there is much theoretical effort to explain the proton puzzle. Such as, the pion cloud and the one-gluon exchange interaction shift the quark spin into the orbital angular momentum,QCD gluon correction, strange quark spin contribution and the SU（3） breaking of octet axial charge 8a, etc. Current data point to the picture where the proton spin puzzle is a valence quark effect. Valence quark contributions to 0a approximately saturate the measured value. Sea quark and QCD gluon corrections to the singlet axial-charge are small within the expectations of quark models.The explanation of these nucleon structure observables has its basis in QCD which is invariant under chiral transformations provided that quarks are massless. Furthermore, chiral effective field theory, an effective low-energy theory of QCD, assumes that the Goldstone Boson of the theory is the effective meson-field, which more properly should be considered a coherent state of quarks and anti-quarks. That virtual meson emission and absorption can play a major role in the properties of hadrons. The chiral effective field theory is more systematical theory and based on the same chiral symmetry of QCD, which is different from commom phenomenological models. The chiral effective feild theory has been widely used in the hadron physics, and there are many successful applications in the study of hadron spectrum and hadron structure. Consideration of the general features of QCD evolution led to the conclusion that the natural scale at which to match a quark model to QCD is quite low, so that most of the momentum of the proton is carried by valence quarks and one can think of the gluons as having been integrated out of the theory. In Jaffe’s scenario（1987）, the small value of the experimental proton spin is due to differences in the energy scale of the experimental result and the quark model results. Thus we calculated the spin of the proton and axial charges of other octet baryons in chiral effective field theory.Proton spin is investigated in chiral effective field theory through an examination of the singlet axial charge, 0a（corresponding to spin Σ）, and the two non-singlet axial charges, a₃ and a₈. The three axial charges of other octet baryons are calculated in chiral effective field theory. Finite-range regularization is included, which has more advantages over the traditional regularization approaches. Baryon octet and decuplet intermediate states are included to enrich the spin and flavor structure of the nucleon, redistributing spin under the constraints of chiral symmetry. Although it lies outside the framework of chiral effective field theory, the effect of one-gluon-exchange（OGE） is particularly important for spin dependent quantities. Therefore it is also included in our calculation.The non-singlet charges, a₃ and a₈, and the singlet charge 0a are obtained simultaneously for each quark-sector contribution is calculated separately in our calculation. In this context, the proton spin puzzle is well understood with the calculation describing all three of the axial charges reasonably well, in well accordance with the measured results from experiments, which is superior to other models where only some axial charge（s） is（are） explained well. The following are main conclusions:1, The parameter reflecting the role of relativistic and confinement effective and constrained by a₃=1.27 is around 0.88, smaller than 1 as expected in na?ve quark mode but larger than the typical “ultra-relativistic”value of 0.65. There are very few parameters in our calculation, the above one is the only one, better than other models and shows the reliability of the calculations. a₈, a₀ were calculated with this parameter.2, SU（3） octet axial charge is in good agreement with the value extracted under the assumption of SU（3） symmetry from hyperon β decay measurement.3, At low energy scale to match a quark model to QCD, the singlet axial charge , and the quark contributions?u 0.91, ?d^-0.36, ?s^-0.01. The total quark spin contribution to the proton spin is reduced to about a half of that expected in the na?ve quark model under the relativistic, meson clouds and OGE effects.4, Because the anomalous dimension of the singlet axial current is nontrivial, the singlet axial charge is scale Q² dependent. With appropriate Q² evolution, we find that the singlet axial charge at the experimental scale, consistent with the current experimental value ⁰.35. Our calculation provides an accurate quantative description of the evolution, with regard to the former model（Jaffe’s） provided just a qualitive description of it, and the evolution results show that our calculation provides a reasonable explanation to the proton spin puzzle.5, The strange quark contribution to the proton spin is negative with magnitude 0.01, which is consistent with the experimental measurements.Our model provides significant insight into the proton spin puzzle. The relativistic, meson clouds and OGE effects transfer the quark spin of the proton to the orbital angular momentum, and produced experimental measurement value with the proper evolution. Each quark spin contribution has been calculated, which provides a cognition of the structure of the proton. While varying the coupling constants D, F, C, and the form of the regulator functions, the values are still in the range of our error bar, which means our model is stable.Axial charges of other octet baryons are also calculated in the same way as for the case of proton spin with the low energy spin constant of proton. The isovector axial charges are, compared with other theoretical calculation results and the lattice rusults, which means our calculation is reasonable. For octet axial charge our results are . At low energy scales the total quark spin contribution to the octet baryons are about 50（25） 60% in valence region, which is similar with the proton’s, and about 0.35 after evolved to the experimental measurement scale 23 Ge V. Each flavor quark spin contribution of the baryons is analogous with the proton case, where the constituent quark flavors（u, s quarks of Σ, （?）） are dominant, and the sea quark flavors（d quark of Σ, （?）） contributions are small with the order of 0.01-0.02, opposite with the spin polarized direction of the baryons.